A variable area volumetric flow rate meter, hereafter simply VA flowmeter, uses a vertical sensing duct through which flows a fluid whose volumetric flow rate is to be measured. The sensing duct has a cross section area that smoothly increases along the length of the sensing bore, typically increasing upwards but that may also increase downwards. Typically, the fluid flows into an end of the duct having the smaller cross section area, and out of the duct at the larger cross section area although variations on this design are possible.
In any duct of changing cross section area, velocity at each point along the duct, of a fluid flowing in the duct varies inversely to the area at that point. While the situation is somewhat different for flow of a compressible gas in such a duct, for low flow velocities generally the velocity will also decrease as duct area increases.
The sensing duct for such a flowmeter contains a float occupying a fraction of the duct area. Normally, the specific gravity of the float is somewhat higher than the fluid flowing in the duct, so the term “float” is a bit misleading. When dealing with liquids however, it is actually possible to use a float that does float.
Fluid flowing through the duct and past the float creates drag force on the float that lifts it from the bottom of the duct. The drag force depends on the fluid velocity around the float, increasing with increasing flow velocity of course.
The float will rise or fall to a point where the drag created by the velocity of the adjacent fluid flowing past the float exactly equals the gravitational force provided by the float less the buoyant force on the float applied by the fluid in the duct. Regardless of the volumetric flow rate in the duct, the float will always reach the point in the duct where the velocity of the adjacent fluid exactly balances the net of float weight less buoyant force on the float. The product of the area of the duct where the float finds equilibrium and the velocity of the fluid adjacent to the float equals the volumetric flow rate of fluid through the duct.
If the fluid is a gas, buoyancy force is very small, indeed may even be ignored, and the gravitational force predominates. If the fluid is a liquid, the buoyancy force may be significant. In an upwardly diverging duct through which a liquid flows, relative specific gravities of the liquid and the float are important in determining the float position for a given flow rate. A downwardly diverging duct with a float whose specific gravity is less than the liquid in the duct is most useful for measuring small liquid flow rates because buoyancy and gravity forces oppose creating a relatively small net force. Normally, the float specific gravity will be larger than that of the fluid, perhaps substantially larger in the case where the fluid is a gas.
Where fluid flow is measured in an upwardly diverging duct, the float specific gravity is normally greater than that of the fluid. The fluid itself; the specific gravity, shape, size, and total weight of the float; and the duct geometry should all be chosen so that the available range of the float's vertical position in the duct allows the expected range of flow rates to be measured.
The flow rate can be calibrated against the float position to accurately indicate the flow rate. In the simplest situation, an operator provides several different known fluid flow rates to the flowmeter and records the position of the float for each flow rate. This provides a table in which the operator can interpolate to determine the flow rate with good accuracy.
Some applications for these flowmeters require them to handle corrosive fluids without contaminating the fluid flowing through the flowmeters. For most of these types of fluids, materials exist that are inert with respect to the fluid. All of the flowmeter surfaces in contact with the fluid must comprise such inert material to avoid contaminating the fluid.
Determining the float position in the sensing duct is sometimes difficult. Magnetic position sensing requires magnetic material in the float. Corrosive fluids may attack such magnetic materials. Even if the magnetic material is completely embedded in the float, users are concerned that the corrosive fluid may penetrate the float and cause contamination.
Alternatively, an optical or other sensor may be located along the length of the sensing duct, but such a sensor must be quite large and complex. Such sensing requires the sensing duct to be made of transparent material, or at least have a transparent window along the sensing duct length, which complicates the sensing duct structure.